The paper is devoted to the study of some important types of minimal artinian linear groups. The authors prove that in such classes of groups as hypercentral groups (so also, nilpotent and abelian groups) and FC-groups, minimal artinian linear groups have precisely the same structure as the corresponding irreducible linear groups. 2000 Mathematics Subject Classification. 20E36, 20F28. Let F be ...

INFINITE LOCALLY FINITE GROUPS OF TYPE PSL(2, K) OR Sz(K) ARE NOT MINIMAL UNDER CERTAIN CONDITIONS JAVIER OTAL AND JUAN MANUEL PENA In classifying certain infinite groups under minimal conditions it is needed to find non-simplicity criteria for the groups under consideration . We obtain some of such criteria as a consequence of the main result of the paper and the classification of finite simpl...

We discuss the approximability of locally compact groups by finite semigroups and finite quasigroups (latin squares). We show that if a locally compact group G is approximable by finite semigroups, then it is approximable by finite groups, and thus many important groups are not approximable by finite semigroups. This result implies, in particular, the impossibility to simulate the field of real...